Board of Governors of the Federal Reserve System

January 17, 2020

Goods-Market Frictions and International Trade

Pawel M. Krolikowski and Andrew H. McCallum

1 Introduction
The difficulty of locating and building connections with overseas buyers is a prevalent firm-level barrier to exporting.¹ Producers and retailers must spend time and resources to find one another before they can transact.² In this note, we formalize these trade barriers as a search friction between exporting producers and importing retailers.³ This goods-market friction results in a fraction of producers, and the goods they produce, being unmatched with retailers and therefore unavailable for purchase by consumers. The unmatched rate of producers is endogenously determined.⁴ We examine the welfare costs of this search friction, as well as what the existence of this friction does to the effects of tariff increases on an economy.⁵

Our formalization delivers three key insights. First, search frictions directly reduce trade flows because a fraction of products are not traded, negotiated import prices "at the dock" are lower than final sales prices, and entering foreign markets is more costly. Second, search frictions also magnify any negative effects of tariff increases on trade flows by deterring retailer entry. Third, even though tariff increases have the usual costs of "protectionism," with search frictions, there is also a substantially offsetting positive effect of protectionism absent from standard trade models that arises because protecting the domestic market makes it easier for domestic producers to meet domestic retailers. By itself, this effect raises welfare, offsetting some of the reduction to welfare from higher tariffs.

When calibrated to U.S and Chinese data, our model implies that search frictions play an important quantitative role for welfare, trade flows, and the import elasticity of tariff increases. We find that reducing international search costs to their domestic levels would increase U.S. and Chinese welfare by 1.4 and 2.6 percent, respectively. Search frictions also double the import elasticity of tariff increases but because of the positive effect on the matching of domestic retailers and domestic producers, these frictions still substantially attenuate the welfare responses to adjustments in tariffs by around 85 percent. Lastly, increasing retailers' average search costs for international matching mimics the negative effects on welfare and trade flows similar to that of a 10 percent increase in bilateral tariffs.

2 Model
Our model features many countries and representative consumers that have utility over goods from all countries. Countries are "segmented" into destination-origin pairs, but these pairs have effects on other pairs through changes in equilibrium values of variables. We assume that consumers can access differentiated goods only via ex-ante homogenous intermediaries called retailers. Producers differ by productivity, and a costly process of search governs matching between producers and retailers.⁶ Market tightness – defined as the ratio of the number of searching retailers to the number of searching producers in a given market – determines the probability of contact for retailers and producers. For example, if there are many unmatched retailers relative to unmatched producers, market tightness is high and producers find a retailing partner quickly. Consistent with segmented destination-origin markets, we assume that searching or matching in one market does not directly affect the costs of searching across others or of future search in the same market.⁷ We assume that every matched producer matches with one, and only one, retailer.⁸

The retailing and producing firms use backward induction over two stages to maximize their value. Assuming that retailers and producers have met in the first stage, in the second stage they bargain over the "negotiated price" and the equilibrium quantity to trade. The negotiated price is a convex combination of the final sales price that consumers will pay and the average total production cost less producers' search costs. The equilibrium quantity traded within matches ensures that the marginal revenue from the consumer is equal to marginal production cost and is the same quantity as in a model without search frictions.⁹

Although the quantity exchanged within a trading partnership does not depend on search frictions, these frictions do affect the number of trading relationships that form. Since producers differ by productivity, they have a productivity threshold that determines if they search or not. This threshold is determined by total variable profits earned from consumers and on producers' "effective entry cost." The effective entry cost includes: the fixed cost of production, the flow cost of searching for a retail partner, the opportunity cost of not searching; and the sunk cost of starting up a trading relationship.

3 Calibration and Quantitative Results
To calibrate the model we proceed in two steps. First, we externally calibrate parameters that can be normalized or that are standard in the literature and do not need to be determined within the model. Second, we internally calibrate the remaining parameters by solving a mathematical program with equilibrium constraints (MPEC).¹⁰ MPEC simultaneously recovers parameters of a model and solves for the accompanying equilibrium endogenous variables to match U.S. and Chinese data. These data include economic aggregates, such as consumption and GDP, business start-up costs, and trading partner separation rates, among other measures. Retailers' search costs are informed by manufacturing capacity utilization rates and the fraction of exporting firms in the two countries.

To gauge the importance of search frictions on welfare in our calibrated model, we conduct an exercise in which we reduce retailers' international search costs to the level of domestic search costs, which in the calibration are lower than the international costs. Column (2) of table 1 reports that the value of imports into the United States from China increases by 210 percent, and the value of imports into China from the United States rises by about 500 percent. Welfare in the United States is 1.4 percent higher and welfare in China rises by 2.6 percent.¹¹

Table 1: Changes in welfare, imports, and the unmatched rate when search frictions are reduced

Our earlier analytic results (Krolikowski and McCallum, 2019, proposition 5) suggest that search frictions would attenuate negative changes in welfare from tariff increases because, as noted earlier, raising tariffs in the presence of these frictions protects the domestic market and makes it easier for domestic producers to meet domestic retailers. Our simulations from the calibrated model suggest that search frictions attenuate the welfare response to a 10 percent tariff increase by a substantial 85 percent relative to a model without search frictions. Column (1) of table 2 shows that without search frictions, Chinese welfare (the last row) falls by 1.8 percent in response to a 10 percent tariff increase on U.S. goods imports. This reduction in welfare shown in the first row is governed by an inefficient increase in the consumption share of domestically produced goods and is consistent with the results in Arkolakis et al. (2012). Column (2) of table 2 shows that in the model with search frictions, Chinese welfare falls by much less, just 0.3 percent (which is about 85 percent less than the 1.8 percent mentioned above) when China raises unilateral tariffs on U.S. goods by 10 percent.

Table 2: Decomposing the Chinese welfare response to a unilateral tariff increase

Decomposing China's welfare reduction using our analytic results show that welfare changes for three reasons. First, the domestic consumption share rises by about 3.7 percent because foreign goods are more expensive after the tariff increase and this reduces welfare to 99.7 percent of the pre-tariff level.¹² Second, the tariff raises the value of being a matched retailer in the Chinese market and leads to more retailer entry and a higher matched rate for Chinese producers. This higher matched rate serves to lessen some of the reduction in welfare caused by more expensive foreign goods. This positive effect on the domestic search market is the protectionism effect. Quantitatively, the tariff raises the domestic market matched rate by 0.6 percent, which boosts welfare by 0.06 percent. Third, the change in Chinese aggregate consumption is quantitatively trivial in both the model with and the model without search.

Table 3 shows that search frictions almost double the responsiveness of trade flows to tariffs, the "import elasticity," relative to a model without search frictions (from -5.3 to -11.9 as shown in the last row) because the change in the international producer matched rates magnifies the effects of a tariff increase. In our calibrated model without search frictions, a 10 percent unilateral tariff on imports into the United States from China reduces the U.S. foreign consumption share by about 50 log percent, implying the import elasticity is negative 5.3 (table 3, column 1). Comparing this to our model with search frictions, the import elasticity is negative 11.9 (table 3, column 2). The main difference between these elasticities is that higher tariffs reduce the benefit to Chinese retailers of being matched with U.S. producers, leading to less Chinese retailer entry, fewer U.S. producers that are matched with Chinese retailers, and even lower imports than in a model without search frictions.

Table 3: Decomposing the Chinese consumption and trade elasticities

Earlier, we discussed the effects of equalizing the search costs of international matching to those of domestic matching. Now we want to highlight that a small increase in retailers' international search costs can have a large effect on welfare and trade. The first column of table 4 shows the welfare losses associated with a 10 percent increase in bilateral tariffs in a model without search costs. The United States experiences a 0.4 percent reduction in welfare, whereas China's welfare falls by 0.3 percent, which we deem to be significant negative welfare effects. Column 2 shows that it takes just a 6 percent increase in international search costs to replicate the results of a 10 percent bilateral tariff increase in the absence of search frictions.

Table 4: Changes in welfare, imports, and the unmatched rate in response to tariff and search cost changes

Our framework and the results presented in our calibrated experiments share the central tenet of any search model: in equilibrium, there exists some number of unmatched exporters who are actively looking for importing partners in the foreign economy. This simple observation leads to profound implications because the product varieties associated with these unmatched exporters cannot be consumed and therefore affect welfare, the price index, trade flows, and the levels of other aggregates. Additionally, if the mass of unmatched producers is endogenous, the absence of these varieties affects not only the levels of aggregates, but also their changes, as we have shown.

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